Off the top of my head and untested:

while (my $row = $parser->fetch()) { 
    my $myColumn_value = $row->{'myColumn'};
    print $myColumn_value unless($myColumn_value eq "");
}
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if (and unless) can act as statement modifiers in Perl, so this will cause the print to be executed only if $myColumn_value isn't equal to the empty string.

You will get a warning here if it's undefined, BTW. If that's an issue, use

    print $myColumn_value unless(($myColumn_value // "") eq "");
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instead.